This reminds me of that which I have been hearing from fish vets for may years. Basically chronic stress has bad effects on fish. Anti anxiety drugs sounds like the opposite of that.
Among the main effects of stress are suppression of the immune system, which can make the fish more susceptible to infections.
I met a researcher on fish stress once. the main way they stressed fish for their experiments was to net them, hold them in the net for a few seconds and then release them. this resulted in a stress response that lasted several hours (as determined by cortisol release).
Interestingly, this stress response could be eliminated by feeding the fish after they were released. The food is a positive re-enforcer. After a few trails the fish no longer had a stress response to being netted.